Nonlinear wave control in an alpha-helix proteins with an impurity: mechanisms of localization, trapping and transmission of breathers

Abstract: This paper studies a one-stranded α-helix of a protein chain in the presence of diagonal and off-diagonal couplings under the control of a mass impurity. Using the semi-discrete approximation and the multiple time scale method, we derive discrete and semi-discrete nonlinear Schrödinger equations. Through the phenomenon of modulational instability, the analysis of linear stability is carried out. A numerical analysis of modulational instability predicts the propagation of solitonic breather-like structures within the system under the simultaneous effect of the mass impurity and the off-diagonal coupling parameter. Furthermore, a numerical study of the impurity mode reveals that indeed the dynamics of the system is characterized by the propagation of solitary breather-like waves. Furthermore, our exploration of the interaction between the breather and the impurity mode reveals a series of physical phenomena, including trapping, reflection, and transmission. Finally, the localization associated with modulational instability in the α-helix is well described, aligning analytical predictions with numerical simulations.